Solve for $x$ and $y$ using elimination. ${2x+6y = 60}$ ${-2x+5y = 39}$
Answer: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $2x$ and $-2x$ cancel out. $11y = 99$ $\dfrac{11y}{{11}} = \dfrac{99}{{11}}$ ${y = 9}$ Now that you know ${y = 9}$ , plug it back into $\thinspace {2x+6y = 60}\thinspace$ to find $x$ ${2x + 6}{(9)}{= 60}$ $2x+54 = 60$ $2x+54{-54} = 60{-54}$ $2x = 6$ $\dfrac{2x}{{2}} = \dfrac{6}{{2}}$ ${x = 3}$ You can also plug ${y = 9}$ into $\thinspace {-2x+5y = 39}\thinspace$ and get the same answer for $x$ : ${-2x + 5}{(9)}{= 39}$ ${x = 3}$